Designing Water Balance Covers (ET Covers) for Landfills and Waste Containment by Craig H. Benson, PhD, PE, DGE, NAE Geological Engineering University of Wisconsin-Madison Madison, Wisconsin 53706 USA    chbenson@wisc.edu

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Covers & Waste Containment Cover system Gas vent or collection well Groundwater monitoring well Waste Native soil Groundwater Leachate collection system Barrier system

Cover Strategy - Conventional vs. Water Balance Covers Conventional Cover Water Balance Cover

Cover Profiles for Water Balance Covers Monolithic barrier: thicker layer of engineered fine-textured soil – “storage layer.”   Capillary barrier: fine-textured soil “storage layer” over coarse-grained capillary break.

What Drives Interest: Cost Savings Subtitle D composite at site: 450 mm fine-grained soil < 10-5 cm/s, 1-mm geo-membrane, drainage layer, and 300 mm surface layer. > 64% cost savings with water balance cover

Water Balance Covers: How They Work Precipitation Evapotranspiration Infiltration “Sponge” L S = soil water storage Sc = soil water storage capacity Percolation if S > Sc

The Balance in Water Balance Covers Storage capacity of cover, Sc Natural water storage capacity of finer textured soils.   Water removal by evaporation and transpiration. Key: Design for sufficient storage capacity to retain water accumulating during periods with low ET with limited or desired percolation. Need to know required storage, Sr.

Real Data More Complex – But Predictable

Soil Water Retention In Unsaturated Soil Suction, y - + 5 1 5 4 3 2 Wilting point Suction, y - + 4 Field capacity - + 3 - + 2 Volumetric Water Content, q As the soil becomes drier, the water filled pathways become narrower and more tortuous - + 1

Unsaturated Hydraulic Conductivity Water retreats into smaller pores as suction increases, causing water content (q) to diminish and hydraulic conductivity to drop.

Unsat. Hydraulic Conductivity & Suction Water retreats into smaller pores as suction increases, causing water content (q) to diminish and hydraulic conductivity to drop. Coarser soil becomes less permeable than drier soil when suction is high enough WET SOIL DRY SOIL

Evaporation and Transpiration (ET) PET = potential evapotranspiration = max ET for given meteorological condition

Potential Evapotranspiration (PET) FAO Penman-Monteith Reference Evaporation (PET) in mm/d http://www.fao.org/docrep/x0490e/x0490e07.htm#solar%20radiation e = atmospheric vapor pressure at 2 m (= saturated vapor pressure x relative humidity), [kPa] es = saturated vapor pressure [kPa] of air at 2 m at air temperature Ta [oC] U = wind velocity at 2 m above ground surface [m/s] x = psychometric constant [kPa/oC] D = slope of curve relating es and T [kPa/oC] Rn = net radiation [MJ/m2-d] = net solar radiation (Rns) – long wave radiation (Rnl) G = soil heat flux [MJ/m2-d] T = atmospheric temperature (oC) 1 MJ/m2-d of energy = 0.408 mm/d water evaporation.

Design Process Define performance goal (e.g., 3 mm/yr) Evaluate local vegetation analog Species distribution and phenology Coverage Leaf area index Root depth and density Evaluate candidate borrow sources What types of soils? How much volume? Uniform? Blending required or helpful?

Design Process - 2 Laboratory analysis on borrow source soil Particle size analysis Saturated hydraulic conductivity Soil water characteristic curve Shrink-swell, wet-dry, pedogenesis Preliminary design computations Required storage Available storage and required thickness Water balance modeling Typical performance Worst-case performance What if scenarios?

Design Process - 3 Final Design Geometric design Surface water management Gas management Erosion control strategies Specification preparation Regulatory approval Bid preparation & contractor selection

Design Questions for Step 5 How much water needs to be stored? Identify critical meteorological years Define precipitation to be stored How much water can be stored? Define the storage capacity Compute required thickness Can water can be removed? Define wilting point Determine available capacity

Required Storage: Design Year Typical Design Scenarios: Wettest year on record 95th percentile wettest year Typical year Wettest 10 yr period Entire record Year with highest P/PET Snowiest winter Combinations

Water Accumulation: When & How Much 1. Determine when water accumulates. 2. Define how much water accumulates. Example: for fall-winter months at sites without snow, water accumulates in the cover when monthly P/PET exceeds 0.34.

Thresholds for Water Accumulation Examined P, P/PET, and P-PET as indicators of water accumulation and found P/PET threshold works best. Data segregated into two climate types (with & without snow and frozen ground) and two periods in each year (fall-winter and spring-summer). Water accumulates when P/PET threshold exceeded. Climate Type Season Threshold No Snow & Frozen Ground Fall-Winter P/PET > 0.34 Spring-Summer P/PET > 0.97 Snow & Frozen Ground P/PET > 0.51 P/PET > 0.32 Fall-winter = September - February Spring-summer = March - August

Example: Idaho Site (snow & frozen ground) Mar-Aug: 0.51 Sept-Feb 0.32

Example: Texas Site (no snow & frozen grd.) Mar-Aug: 0.97 Sept-Feb 0.34

How Much Water Accumulates? 1. Use water balance approach: ΔS = P – R – ET – L – Pr Δ S = change in soil water storage R = runoff P = precipitation ET = evapotranspiration L = lateral internal drainage (assume = 0) Pr = percolation 2. ET is unknown, but is a fraction (β) of PET: ET = β PET 3. R, L, and Pr can be lumped into losses (Λ) Simplify to obtain: ΔS = P – β PET – Λ 4. Equation used to compute monthly accumulation of soil water storage if P, PET, β, and Λ are known.

Parameters for Water Accumulation Equation Δ S = P – β PET – Λ Climate Type Season β (-) Λ (mm) No Snow & Frozen Ground Fall-Winter 0.30 27.1 Spring-Summer 1.00 167.8 Snow & 0.37 -8.9 Two sets of β and Λ parameters (fall-winter & spring-summer) for a given climate type.

Monthly Computation of Required Storage Fall-Winter Months Spring-Summer Months Sr = required storage Δ Sr m = monthly water accumulation hm = monthly index for threshold (0 = below, 1 = above) If Δ Sr m < 0, set Δ Sr m = 0.

Computing Required Storage Fall-Winter Months Spring-Summer Months If argument < 0, set = 0 βFW = ET/PET in fall-winter βSS = ET/PET in spring-summer ΛFW = runoff & other losses in fall-winter ΛSS = runoff & other losses in spring-summer Pm = monthly precipitation PETm = monthly PET

Example: Idaho Site (snow & frozen ground) For months below threshold, set ΔS = 0 Δ S = P – 0.37*PET (Fall-Winter) β = 0.37, Λ = 0 Store 97 mm for typical year, 230 mm for wettest year

Example: Texas Site (no snow & frozen ground) For months below threshold, set ΔS = 0 ΔS = (P – 0.37*PET)-27 (Fall-Winter) β = 0.3, Λ = 27 Store 188 mm for 95th percentile year, 548 mm for wettest year

Predicted and Measured Sr Good agreement computed & measured required storage.

Monolithic Covers: Storage Capacity What is the storage capacity (Sc)? Area qc = water content when percolation transmitted.

Monolithic Covers: Storage Capacity What is available storage (Sa)? qmin = lowest water content achieved consistently. Area

Soil Water Characteristic Curve (SWCC) qfc = field capacity water content, qfc at 33 kPa suction (use for qc). qwp = wilting point water content, q at 1500 kPa. Arid regions 4000-6000 kPa. (use for qmin). qwp = qfc - qwp = unit storage capacity. 4000 kPa 33 kPa qfc = 0.26, qwp = 0.01, qu = unit storage = 0.26-0.01 = 0.25

Pedogenesis & Hysteresis Lab curve on small compacted specimen, typically ASTM D6836 Field curve has lower air entry suction and steeper slope. qs = saturated q qr = residual q a = shape parameter controlling air entry suction n = shape parameter controlling slope

Compare: Field to Lab Create field SWCC by adjusting lab-measured SWCC: a adjustment Plastic soils = 13x Non-plastic soils = none n = no adjustment

Compare Field-Measured & Computed Storage Capacities from ACAP Good agreement between computed and field-measured storage capacities. Need to account for effect of pedogenesis on soil properties.

Design Step 6 – Water Balance Modeling Webinar March 14 T E P R q Pr z

Why model water balance covers? Predict performance relative to a design criterion and/or refine design Sensitivity analysis to determine key design parameters Comparison between conventional and alternative designs. “What if?” questions. For these purposes, model MUST capture physical and biological processes controlling behavior (e.g., unsaturated flow, root uptake)

Output: Water Balance Quantities Precipitation: water applied to the surface from the atmosphere (unfrozen and frozen) Evaporation: water discharged from surface of cover to atmosphere due to gradient in vapor pressure (humidity) Transpiration: water transmitted to atmosphere from the soil via plant root water uptake Evapotranspiration: evaporation + transpiration Infiltration: water flowing into soil across the surface

Predictions for 2001-2003 for a site in Altamont, CA using LEACHM Sample Output Predictions for 2001-2003 for a site in Altamont, CA using LEACHM Predictions appear realistic, but are not real. All models are mathematical abstractions of reality. Apply appropriate skepticism to predictions.

Appendix

PET Calculations - 1 Data for Input: Air temperature at 2 m (daily minimum, Tmin, and maximum, Tmax), oC Solar Radiation, Rs (MJ/m2-d) Daily average wind velocity, U, at 2 m (m/s) Daily average relative humidity, RH (%) Soil heat flux, G ~ assume = 0

PET Calculations - 2 x = 0.665x10-3 P where P is atmospheric pressure in kPa P = 101.3 [(293-0.0065z)/293]5.26 , P in kPa and z in m above mean sea level T = mean daily air temperature (oC) at 2 m, [Tmin+Tmax/2] es = 0.6108exp[17.27 T/(T+237.3)] in kPa and T in oC {compute as average of es determined for Tmin and for Tmax} e = es(RH/100), in kPa, where RH is relative humidity in % D = 4098{0.6108exp[17.27 T/(T+237.3)]}/(T+237.3)2 , kPa/oC

PET Calculations - 3 Rns = net solar radiation = Rs (1-a) a = albedo (fraction of solar energy reflected) Rnl = net long wave radiation (emitted from earth) h = Stefan-Boltzman constant (4.903x10-9 MJ/K4-m2-d) Tmin and Tmax in oK Rso = clear-sky solar radiation

For latitude: http://www.bcca.org/misc/qiblih/latlong.html PET Calculations - 4 with z in m above mean sea level Ra = extraterrestrial radiation (MJ/m2-d): J = Julian day (1-365 or 366) For latitude: http://www.bcca.org/misc/qiblih/latlong.html